On simple interest, a certain sum becomes Rs. 59,200 in 6 years and Rs. 72,000 in 10 years. If the rate of interest had been 2% more, then in how many years would the sum have become Rs. 76,000?

Solution(By Examveda Team)

\[\begin{gathered} P\xrightarrow{{{\text{6 years}}}}59,200 \hfill \\ P\xrightarrow{{{\text{10 years}}}}72,000 \hfill \\ \end{gathered} \]
$$\eqalign{ & {\text{Difference 4 years}} \cr & = \left( {72,000 - 59,200} \right) \cr & = 12,800 \cr & {\text{1 year}} = \frac{{12,800}}{4} = 3,200 \cr & \therefore {\text{6 years S}}{\text{.I}}{\text{.}} \cr & = 3,200 \times 6 = 19,200 \cr & P = 59,200 - 19,200 = 40,000 \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{{P \times r \times t}}{{100}} \cr & 19,200 = \frac{{40,000 \times r \times 6}}{{100}} \cr & r = 8\% \cr & {\text{If }}r = 8\% + 2\% = 10\% \cr & P = 40,000 \cr & t = ? \cr & A = 76,000 \cr & \therefore {\text{S}}{\text{.I}}{\text{.}} = 36,000 \cr & 36,000 = \frac{{40,000 \times 10 \times t}}{{100}} \cr & t = 9{\text{ years}} \cr} $$